Interferometric measurements of radii of optical functional surfaces (test surfaces) are commonly based on the Fizeau principle. Coherent collimated light from a source is split on an amplitude splitter surface located in the beam path. The reference wave travels back into itself. The test wave is transmitted through the amplitude splitter surface and reaches the specimen. Using a measuring lens, the shape of the wave can be fitted to different specimens. The amplitude splitter surface generally constitutes the last glass-air interface of the lens for spherical specimens. The test wave is generally fitted to the specimen if all beams of the test wave impinge vertically on the specimen. For a spherical specimen, a focusing measuring lens is used. To measure the surface fit, the specimen is subsequently placed at the distance from the measuring lens at which the center of curvature of the specimen coincides with the focal point of the measuring lens. After passing backward through the measuring lens, the test wave interferes with the reference wave. This type of test is referred to as interferometric null test, and a measuring lens functioning in this manner is a so-called optical null system.
The optical path differences between the reference wave and the test wave lead to an intensity modulation in the measured image (interference fringes). These interference fringes can be distinguished only within an optical path difference of one wavelength of the light used. Thus, the set distance between the measuring lens and the specimen cannot be readily determined. In an interferogram, it is possible to determine the difference in the curvature of the test wave at the site of the specimen but it is not possible to determine the distance of the specimen from the reference surface. Therefore, the absolute radius cannot be calculated from an interferogram.
To determine the radius of curvature of a curved reflecting surface (test surface) based on the Fizeau principle, the surface vertex of the test surface is generally placed in the focal point of the measuring lens (cat's eye position), on the one hand, and at a distance from the focal point which corresponds to the radius of curvature of the test surface (autocollimation position), on the other hand. These two specified positions can be determined very precisely by means of the interferometer since in these positions, interferograms that can be analyzed are obtained (see FIG. 1). In this figure, the cat's eye position is designated by P(cat), the autocollimation position by P(aut) and the radius of curvature by R.
The path of movement between the two positions corresponds to the radius of curvature of the test surface. Since a potential path of movement is limited by the local conditions, this type of measuring setup can be used only to a limited extent for measuring larger radii of curvature. Frequently, the technical limit is approximately 2 m. As to the measurable radii of curvature, it can be used only with a measuring lens for a range of radii if the test surface is a spherical surface.
To test aspheric test surfaces, the measuring lens must be individually fitted to the asphere of the test surface. The manufacture of aspheric measuring lenses that form beams by refraction of the wave entails a considerably greater degree of technical complexity than the manufacture of spherical refraction measuring lenses. Therefore, for the case mentioned, computer-generated holograms are used, often in combination with a Fizeau lens.
The use of this type of measuring setup is therefore limited to test surfaces with small to medium radii of curvature, and it is in practice useful only for spherical and cylindrical test surfaces.
The maximum distance to be set between the measuring lens and the test surface, which distance primarily determines the length of the measuring setup, is invariably greater than the radius of curvature of the test surface.
If the test surfaces to be tested are concave, this distance results from the sum of the focal length of the measuring lens and the radius of curvature of the test surface.
If the test surfaces to be tested are convex, this distance corresponds to the focal length of the measuring lens which must be greater than the radius of curvature of the test surface.
Theoretically, the length of the test setup could be shortened by using a measuring lens with a negative focal length. In practice, however, this leads to a virtual focal plane in which an arrangement of the test surface is not possible, and thus, it is also not possible to determine a path of movement, from which the radius of curvature can be derived.
As already mentioned, with respect to the measurable radius of curvature, the same limitation applies to spherical test surfaces and aspheric test surfaces alike, with the added problem that for each aspheric test surface that is to be tested, a specific measuring lens must be created, which lens must be able to transform a specific aspheric wave.
Instead of refractive measuring lenses, diffractive optical elements are generally used to test aspheric test surfaces.
Such diffractive optical elements can be, in particular, substrate plates, on the image-side surface of which a computer-generated hologram (CGH) is created. In this case, the CGH serves as an optical null system and deflects the test wave by diffraction in such a manner that this test wave impinges vertically on the aspheric test surface to be tested, is reflected back from this surface and is back-transformed by the CGH. A separately guided reference wave is subsequently superimposed on the test wave.
In measuring setups of this type, the substrate quality of the CGH and the quality of the other optical elements used in the interferometer, among other things, limit the accuracy of measurement.